In drilling and logging operations, sonic measurements can be used to determine characteristics of a geological formation. Sonic measurement techniques generally employ a sonic measurement tool including one or more acoustic transmitters and multiple sensors arranged along the tool. The sensors are arranged to obtain a multidimensional sonic waveform including multiple individual sonic waveforms, also referred to as acoustic waveforms, which have propagated from the acoustic transmitter(s), through the geological formation, and to the sensors at various depths and azimuthal directions. The signal components, or modes, and associated characteristics of the sensed, multidimensional sonic waveform can be used to characterize the formation. In applications in which the number of tool sensors is large, and/or the number of azimuthal directions supported by the tool sensors is large, the amount of sonic data sensed by the tool and to be reported to a surface monitoring station can be large and consume most or all of the available telemetry bandwidth. Accordingly, in some applications, compression is used to reduce the amount of sonic data to be reported by the sonic measurement tool via the telemetry link.